Electricity: Class 10 Science · Chapter 11

Think of the moment the power comes back after a cut on a summer evening. Fans begin to turn, tube lights flicker on, a phone left on charge lights up, and someone checks that the fridge is humming again. Every one of these runs on the same thing: electric charge pushed round a closed path by a source of energy.

In this chapter you will find out what an electric current is, what makes it flow and what controls its size. You will meet Ohm's law and see how resistors behave when they are joined in series and in parallel. Finally you will see why a current heats a wire, how much power appliances use, and how an electricity bill is worked out.

11.1 Electric Current and Circuit

Press a doorbell switch and the bell at the far end of the corridor rings at once. Something has been set moving through the wires: electric charge. A steady flow of charge is an electric current (विद्युत धारा). In metal wires the charges that move are electrons.

Notice that a doorbell needs two wires, not one. Charge leaves the supply, passes through the bell and returns to the supply: it needs a complete route. An unbroken conducting loop from one terminal of a source round to the other is an electric circuit (विद्युत परिपथ). A switch is simply a gap in the loop that you can open or close. Open it, and the flow stops in every part of the loop together; close it, and it starts everywhere together (Fig. 11.1).

Which way does a current go? The rule we still use was fixed in the early days of electrical science, more than a century before the electron was discovered in 1897: current is taken to leave the positive terminal of the source, go round the circuit and return to the negative terminal. This is called conventional current. Electrons are negative, so in a wire they actually drift the other way, from − to +.

How big is a current? We count how much charge crosses any cross-section of the wire every second. If a charge $Q$ passes in a time $t,$ the current is

Charge is measured in coulombs (C). One electron carries only $1.6\times {10}^{-19}\mathrm{C},$ so a single coulomb is the charge of about $6.25\times {10}^{18}$ electrons. The unit of current, the ampere (A), honours André-Marie Ampère (1775–1836) of France. A current of $1\mathrm{A}$ means one coulomb of charge passing each second, so $1\mathrm{A}=1\mathrm{C}\mathrm{/}\mathrm{s}\mathrm{.}$ Small currents are given in milliamperes, $1\mathrm{m}\mathrm{A}={10}^{-3}\mathrm{A},$ and microamperes, $1\mu \mathrm{A}={10}^{-6}\mathrm{A}\mathrm{.}$

Current is measured with an ammeter (ऐमीटर). The current has to pass through the meter to be counted, so an ammeter is always joined in series: you open the circuit and close it again through the meter. In Fig. 11.1 the ammeter sits in the bottom wire. In a single loop its reading would be the same wherever you put it.

11.2 Electric Potential and Potential Difference

A copper wire is packed with free electrons, yet on its own it carries no current. Something has to push the charges along. Picture water in a closed loop of pipe (Fig. 11.2). If nothing drives it, the water just sits there. Switch on a pump and it creates a difference in pressure: water leaves the pump at high pressure, flows round the loop, and comes back at low pressure to be pushed again.

In a circuit the cell plays the part of the pump. Chemical reactions inside it push charge towards one terminal and away from the other, so the two terminals differ in electrical 'pressure'. That difference is the potential difference (विभवांतर), or p.d. A new cell on a shop shelf already has it. Join a circuit, and the p.d. drives charge round: every coulomb collects energy inside the cell and hands it over in the bulb. The energy comes from the cell's chemicals, which is why cells run down. Two or more cells joined together make a battery.

So p.d. is measured as energy per unit charge. If carrying a charge $Q$ between two points takes work $W,$ the p.d. between those points is

The unit of p.d. is the volt (V), honouring the Italian physicist Alessandro Volta (1745–1827). When $1\mathrm{J}$ of work moves $1\mathrm{C}$ of charge between two points, the p.d. between them is one volt:

So a $1.5\mathrm{V}$ cell hands $1.5\mathrm{J}$ of energy to every coulomb that passes through it. P.d. is measured with a voltmeter (वोल्टमीटर), which is always joined in parallel: its two leads touch the two points, one on each side of the part being tested, without breaking the circuit.

11.3 Circuit Diagram

Sketching a circuit as it really looks takes time and hides what matters. Instead we draw a circuit diagram: each part becomes a simple standard symbol, and wires become straight lines. Anyone who knows the symbols can then read the circuit, whatever language they speak. Fig. 11.3 shows the symbols used in this chapter.

A few habits make diagrams easy to read. Draw wires as straight lines with square corners. Make the longer plate of a cell the positive terminal. Put a dot wherever wires are joined, and leave it out where they only cross. In school labs a plug key often does the switch's job: pushing its brass plug in closes the circuit, and taking it out opens it.

11.4 Ohm's Law

If you double the push, do you double the current? To find out, we need a circuit in which the p.d. can be raised step by step while the current is read each time.

Plotting the readings gives a straight line through the origin (Fig. 11.4). Twice the p.d. gives twice the current, three times the p.d. three times the current, and the ratio V/I never changes.

In 1827 Georg Simon Ohm (1787–1854), a German physicist, reported this pattern for metal wires. It is now called Ohm's law (ओम का नियम).

The constant $R$ tells you how many volts it takes to push each ampere through the conductor. It is called the resistance (प्रतिरोध): the bigger it is, the more strongly the conductor opposes the flow of charge. It is measured in ohms, written Ω (the Greek capital omega). A wire in which every volt drives exactly one ampere has $R=1\mathrm{\Omega },$ so $1\mathrm{\Omega }=1\mathrm{V}\mathrm{/}1\mathrm{A}\mathrm{.}$ Ohm's law can be turned round in two useful ways:

A dimmer for a stage light, the speed control of a toy car and an old fan regulator all do the same job: they change the current while the supply stays the same. Form (11.7) shows how. With $V$ fixed, current and resistance are inversely proportional, so three times the resistance lets through a third of the current. A part whose resistance can be adjusted is a variable resistor. The lab version, a rheostat (धारा नियंत्रक), has a sliding contact that sets how much resistance wire is in the circuit.

The simulation below repeats the activity. Note one difference: it plots current upwards against p.d., so there the steeper line belongs to the smaller resistance (its slope is $1\mathrm{/}R$).

Does every part of a circuit pass the same current from the same source? The next activity compares several.

Why do parts differ? Inside a metal the free electrons cannot glide through: they keep colliding with the vibrating atoms, which slows their drift. How much a part slows the drift is its resistance. The rubber band sits at one extreme: an insulator, with so much resistance that no current can be measured. At the other extreme is a good conductor such as copper, whose resistance is tiny for its size. In between are parts made on purpose with a known, useful resistance, like the nichrome wire and the coil you used: these are resistors.

11.5 Factors on which the Resistance of a Conductor Depends

An electrician uses thick wire for an air conditioner but thin wire for a bedside lamp, and heater coils are never made of copper. These choices depend on how the resistance of a wire changes with its size and with the material it is made of.

Careful measurements on uniform metal wires give two rules. Resistance rises in step with length, $R\propto l,$ and falls as the cross-section grows, $R\propto 1\mathrm{/}A\mathrm{.}$ A longer wire is a longer obstacle course for the electrons; a thicker wire offers more lanes side by side. Putting the two together gives

The constant $\rho$ (Greek rho) is the resistivity (प्रतिरोधकता) of the material. Resistance belongs to a particular wire, but resistivity belongs to the substance. Cut a copper wire in half and its resistance halves, yet its resistivity is unchanged. Rearranging gives $\rho =RA\mathrm{/}l,$ so the unit of resistivity is $\mathrm{\Omega }\times {\mathrm{m}}^2\mathrm{/}\mathrm{m},$ the ohm metre (Ω m).

Look at the spread in Table 11.5. Metals and alloys lie between about ${10}^{-8}$ and ${10}^{-6}\mathrm{\Omega }\mathrm{m};$ insulators such as glass, rubber and quartz lie far above, from about ${10}^{11}$ to beyond ${10}^{17}\mathrm{\Omega }\mathrm{m}\mathrm{.}$ Resistivity also changes with temperature: for metals it rises as they get hotter.

These numbers explain why each job gets its own material:

• Wires and power lines should waste as little energy as possible, so they use the metals of lowest resistivity that are affordable: copper, and aluminium, which is also light.
• Heating elements in irons, toasters and room heaters need a large resistance in a small coil and must stay red-hot for hours. Alloys such as nichrome suit them: an alloy usually has a far higher resistivity than the metals it is made from, and nichrome does not oxidise (burn) easily.
• Bulb filaments must glow white-hot without melting, so they are made of tungsten, which survives temperatures above $3000{}^{\circ }\mathrm{C}\mathrm{.}$

11.6 Resistance of a System of Resistors

Real gadgets rarely hold just one resistor. A radio, a phone charger or the wiring of a house joins many parts together, and there are two basic ways of doing it. In series (श्रेणीक्रम) the resistors are joined end to end in one chain, so charge must pass through each in turn. In parallel (पार्श्वक्रम) every resistor is joined across the same two points, so the charge has a choice of routes. In each case Ohm's law lets us replace the whole group by a single equivalent resistance.

11.6.1 Resistors in Series

Does a resistor 'use up' some of the current, leaving less for the next one? An ammeter moved along a series chain answers this.

11.6.2 Resistors in Parallel

Now join the resistors side by side, each one connected between the same two points X and Y. Every resistor gets its own branch. The charge arriving at X splits up among the branches and joins up again at Y.

Why is nothing in your home wired in series? Picture the five lamps along a school corridor joined in one series chain. They would have to share the $220\mathrm{V},$ so none would get the voltage it was made for. If one lamp burnt out, the only path would break and the whole corridor would go dark (Fig. 11.11). And a lamp could never share a chain with a heater, because the two need very different currents while a series chain forces the same current through both.

In parallel, each appliance sits directly across the supply, so each gets the full voltage and draws only the current it needs. Each has its own switch, and one failure leaves the rest working. Joining more appliances in parallel lowers the total resistance and raises the total current drawn from the supply. That is why house wiring needs limits on current, and fuses.

11.7 Heating Effect of Electric Current

Touch a phone charger after an hour of use: it is warm. A mixer-grinder turns most of its energy into the spinning of its blades, yet its body warms up too. A geyser element is nothing but a resistor, so every joule it receives becomes heat. Whenever a current flows through a conductor that has resistance, some or all of the source's energy is turned into heat. This is the heating effect of electric current.

Notice the square in Joule's law. Doubling the current through the same resistor produces four times the heat, while doubling the resistance or the time only doubles it (Fig. 11.13). For an appliance on a known supply voltage, first find the current from $I=V\mathrm{/}R,$ then use $H=I^{2}Rt;$ or use $H=V^{2}t\mathrm{/}R$ directly.